Efficient computation of lattice Green's functions for models with nearest-neighbour hopping
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Bibliographic record
Abstract
We show that for models with nearest-neighbour (nn) hopping, the lattice Green's functions can be calculated without the need to perform integrals. Our method applies to rectangular, triangular and honeycomb lattices in two dimensions, and to simple, face-centered and body-centered lattices in three dimensions. External magnetic fields can be dealt with trivially. As an example, we show that our method works for any ratio ϕ/ϕ0 of the magnetic flux through the unit cell, i.e. irrespective of the change in the size of the magnetic unit cell. Other straightforward generalizations are to models with multiple orbitals per site, with any spin-orbit coupling, on-site disorder, and any combinations thereof. The method works equally well in the presence of surfaces. In all cases, accurate values for large distances can be obtained very efficiently and without finite-size effects. The relationship to other computational methods is also analyzed.
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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